Gravitational instantons with quadratic volume growth

Abstract

There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG and ALG${}^{\ast }$. Gravitational instantons of type ALG were previously classified by Chen-Chen. In this paper, we prove a classification theorem for ALG${}^{\ast }$ gravitational instantons. We determine the topology and prove existence of "uniform" coordinates at infinity for both ALG and ALG${}^{\ast }$ gravitational instantons. We also prove a result regarding the relationship between ALG gravitational instantons of order $\mathfrak{n}$ and those of order $2$.

26 pages; final version to appear in Journal of the London Mathematical Society

References in corpus (2)

• Asymptotic Geometry of the Moduli Space of Parabolic $SL(2,\mathbb{C})$-Higgs Bundles
• Hodge theory on ALG${}^{\ast }$ manifolds

Cited by in corpus (2)

• Collapsing geometry of hyperkähler 4-manifolds and applications
• The Torelli Theorem for $AL{H}^{\ast }$ Gravitational Instantons